1. Field of the Invention
The present invention relates to a design method for high frequency amplifiers using a power gain-boosting technique and the high frequency amplifiers using the method.
2. Description of the Related Art
At microwave frequencies, the intrinsic gain of an amplifier is insufficient due to parasitics, high loss, low device fmax, etc. Therefore a gain-boosting technique is needed.
Consider the configuration of a high frequency amplifier circuit as shown in FIG. 1. Assume the amplifier core which can be a particular transistor has the following S-parameters:
                    [                                                            S                11                                                                    S                12                                                                                        S                21                                                                    S                22                                                    ]                            (        1        )            
The Transducer Gain GT of the above circuit is defined as the ratio of the power delivered to the load to the power available from the source, and is given as:
                              G          T                =                                            1              -                                                                                      Γ                    S                                                                    2                                                                                                      1                  -                                                            Γ                      IN                                        ⁢                                          Γ                      S                                                                                                  2                                ⁢                                                                  S                21                                                    2                    ⁢                                    1              -                                                                                      Γ                    L                                                                    2                                                                                                      1                  -                                                            S                      22                                        ⁢                                          Γ                      L                                                                                                  2                                                          (        2        )            
Subsequently, the Maximum Available Gain Gmag is defined as the Transducer Gain of an amplifier when both the input and the output are simultaneously conjugately matched as shown FIG. 2:ΓS=ΓIN*  (3a)ΓL=ΓOUT*  (3b)
The equation for Gmag in terms of S-parameters is rather complicated. However, Gmag can be expressed more simply using the concept of the stability factor which is described next.
The stability factor k of an amplifier is expressed as:
                    k        =                              1            -                                                                            S                  11                                                            2                        -                                                                            S                  22                                                            2                        +                                                          Δ                                            2                                            2            ⁢                                                                          S                  12                                ⁢                                  S                  21                                                                                                      (        4        )            
whereΔ=S11S22−S12S21.  (5)
An amplifier is said to be unconditionally stable if and only if the following two conditions are satisfied:|Δ|<1  (6)k≧1  (7)
Otherwise, it is conditionally stable, or potentially unstable. Simultaneous conjugate matching is only possible when the amplifier is unconditionally stable, i.e. when |Δ|<1, and k≧1. For most practical transistors: |Δ|<1, therefore, usually only k alone is enough to check for stability.
The Maximum Available Gain can then be expressed in terms of k:
                              G          mag                =                                                                        S                21                                            S                12                                                          ⁢                      (                          k              -                                                                    k                    2                                    -                  1                                                      )                                              (        8        )            
When k<1, Gmag is nonexistent; instead, another gain which is defined as
              S      21              S      12        is used. This gain is called Maximum Stable Gain Gmsg, which is only a figure of merit. As a result, a plot of Gmag will commonly also include Gmsg to attend to the case when k<1. The denotation Gmsg˜Gmag is therefore used for this kind of plot.
The Maximum Unilateral Gain U, or the Mason's Invariant, is defined as the Maximum Available Gain of a transistor after it has been unilateralized, i.e. when reverse isolation is infinite, or when there is no coupling from the output back to the input (S12=Y12=Z12=0). In other words
  U  =            lim                        S          12                →        0              ⁢                  (                  G          mag                )            .      The original expression of U established by Mason is:
                    U        =                                                                                            Z                  21                                -                                  Z                  12                                                                    2                                4            ⁡                          [                                                                    Re                    ⁡                                          (                                              Z                        11                                            )                                                        ⁢                                      Re                    ⁡                                          (                                              Z                        22                                            )                                                                      -                                                      Re                    ⁡                                          (                                              Z                        12                                            )                                                        ⁢                                      Re                    ⁡                                          (                                              Z                        21                                            )                                                                                  ]                                                          (        9        )            where Z11, Z12, Z21, and Z22 are the Z-parameters of the transistor.
When the amplifier is embedded into any linear, lossless, reciprocal network, U remains constant. U decreases with frequency. When U equals unity, the transistor is said to become passive and no longer function as an amplifying unit. The frequency at which U=1 is called the Maximum Oscillation Frequency fmax, which sets the limit in which the transistor can be of use.
Generally, the feedback from the output to the input due to poor reverse isolation decreases the intrinsic gain of the transistor such that Gmsg˜Gmag is lower than U. A plot of Gmsg˜Gmag and U versus frequency for a particular transistor is shown in FIG. 3. It can be seen that at high frequencies, Gmag drops significantly.